Helical spring



May 11, 1948. 'A' RA'SPET 2,441,167

HELICAL SPRING l original Filed March 27, 1942 atented Maly l1, 1948 vUNITED fsrAri-:s

PATENT OFFICE HELICAL SPRING August Raspet, Locust Valley, N. Y.

1 Claim.

(Granted under the act of March 3, 1883, as amended April 30, 1928; 370 0. G. '757) The invention described herein, if patented, may be manufactured and used by or for the Government for governmental purposes without the payment to me of any royalty thereon.

This ease is a division of my application Serial No. 436,390, illed March 27, 1942, now Patent No. 2,402,666, June 25, 1946.

My invention relates to helical springs ofthe type which wind or unwind upon elongation. These springs have been constructedv empirically with the result that their rotational response to elongation Was not a determinable function of that elongation. Therefore, such springs were not suitable for use in measuring instruments, and their use was especially objectionable in instruments produced in quantity.

An object of this invention is to provide a helical spring the behavior of which can be predicted with mathematical exactness.

The features of the invention are illustrated in the accompanying drawing, wherein:

Fig. 1 is a view in elevation of a helical spring formed of an elastic strip having its widthV par- `allel to the axis of the helix;

Fig. 2 is a view similar to Fig. 1, but showing a spring formed of an elastic strip with its width parallel to the radii of the helix;

Figs. 3, 4 and 5 are graphs illustrating the logarithmic, parabolic and linear responses respectively of helical springs made according to this invention; and

Fig. 6 is a detail view illustrating a -representative group of cross sections of elastic strips which may be used in constructing helical springs.

Helical springs constructed of an elastic strip will wind or unwind when elongated according to the relative rigidity of the cross section of the strip to bending as compared to the sections torsional rigidity. The tendency of such a spring to wind or unwind depends upon .the relative torsional and bending rigidities of the strip, as well as upon the pitch angle and theradius of the helix. Specically this invention proposes to utilize the variation in pitch angle to obtain certain mathematical relationships between the elongation and the amount of turning of the helical spring.

In the illustration Fig. 1 the strip is 'a iiat ribbon wound with its greater cross-sectional dimension parallel to the axis of thehelix. In this configuration of the helical spring the spring tends to unwind when elongated. The basic reason for this behavior lies in the fact that the potential energy of such a spring is stored in the bending and in twisting of the cross section of the strip. In the spring illustrated in Fig. 1

the energy stored in bending the cross section about a radius of the section at that point is greater than that stored in twisting the section. This results in a rotation of the free end of the spring in `such a direction that the spring unwinds.

On the other hand, if the spring is wound as shown in Fig. 2, the spring is more rigid to torsion than to bending in its section and there consequently results a tendency for the spring to wind up.

A more rigorous description of the behavior of a helical spring is that furnished by mathematical analysis. The earliest mathematical analysis of the behavior of helical springs dates to Mossotti 1817. Later, Kirchoff, Thomson and Tait, and Clebsch added their endeavors to the solution of the problem. Formally the treatment of this problem consists in setting up the relation expressing vthe potential energy of the spring in terms of the various parameters. The jpotential energy is differentiated for the incremental rotation and elongation. The resulting relations for a, :dat stripof radial thickness a and longitudinal width b are:

cos2 a where (A) This invention is based on the principle discovered by applicant that from the quotient of the above relations the rotatory magnification Y expressed as turns of the spring per unit elongation can be obtained. The magniiication is found The rotatory magnication is shown by this Y newly discovered relation to be clearly dependent" 10 on the radius R of the spring; thejsntiallerthe radius the greater the magnification. Further.

it can be seen from this relation: that the niagnication will be greatest thefjifaluewfjab. departs substantially from' unity. In' the *case Where Having. attentats l b1l as@ haring. Sessies. amie @mit aceites Where f1 =the total turns of spring, and k is a constant.

From newly. dLSQQversstrelaiiOgs. filari [41 it follows that for thiscgng'itign; l

A solution of the latter equation for@ furnishes the Value 0f the piishiansleniiihs helical 'Spring for which the roiatoryimaeniiisatiilniis inyerssly proportional to the length ofthe spring;` wherefor'e'j the'rotation ofthe ispioportional' to functional i'lationf'wh V"therotation' 4is plotted against the logarithm of the springs length; graphs as a straight line, Fig. 3.

(B-2) In another application of the helical spring described herein one may desire a parabolic 15 relation between the rotation and the length of the spring, viz:

i==cL2 [7] whereis a constant- Y y Sixth 'a'A behavior is attainedl as above shown when thetayirnagniiiatiiobeis'the following relation:

' where h is a constantf'or Solving` the last equation for a Will furnish the ptoh; 'angle `arr0lld 'WI'sh th Ll'll'al spring Will behave linearly: "In the: eld of instrumentation this type of spring ha's"\7vide'ppliiiation'to 'prese tribal ma'slin nstrnts'. A' u (C) For illustrating "tlfeznethod-.described in this invention themathematical"formulaehave been developed. fori "the cas of: a helical" "springJ W'ound vofa flat" ribbon 'ffan'elastic material; It must be emphasized that the methodis'p'erfeotly generalin that; one may'simply'substitute'or. the torsional; 'andftbendingi "energy"l relations' on the flat stripA the relations applying to 'r'oss sections' Qiqlother congurati'onst'Ithappens that' the greatest .maghicationis' obtained by the use of a i i'l'at strip; "ibut i for `"certain applications. other cros'ssectionalfdrms may be desired.: Various cross sections` of.springs 'which Vwif/ill;respond. to

this treatmentare. illustratedin Fig.'6,jcrssseo tions a tog; inclusive. Y

'From the foregoing: description oi preferred ernbodiments of my invention it Willbe readily'apparent to' those skilled the Yarti that' th'einvenL tion is not, limited. to thepartielarenbo'dinents disclosedft'o 4illustriat'etlfiesaine.`

What is claimed is:

A helical spring in? which the` helix angle is so seleoted .itha'tf the.4 rotatoty ..1nagi`catin exl pressed as turnsot the spring p'erunitl elongation is. directly proportionalt its' length; thatsj in 1 r "man in .1s. r -1 T. Hf --FA r ..k ,.Y-J 4 where and (c) is a constant of sensitivity; the equation dq, being:

E (1-6492) is the rotatory magnication" expressed as turns 4011i@ tan a= 1. b a 1 of the spring per unit elongation, L is the length R (tan a+64 E ctn a) of the helix and lc is a constant, where the pitch b q angle (a) is given by solving the equation hereinwhich, when solved for tan a, yields: after following after introducing the selected 3 values of radial thickness (a), the longitudinal lo 1 64(%) 2 width (b), the Youngs modulus (q) and the can a: T-i1 64(9.) shear modulus (n), where R 1s the radius of the WR I b 4 spring, b the total number of turns o1' the spring AUGUST RASPET. 

